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NOAA Technical Memorandum NMFS-NE-110

Length-Length and Length-Weight Relationships for 13 Shark Species from the Western North Atlantic

Nancy E. Kohler, John G. Casey, and Patricia A. Turner
National Marine Fisheries Serv., Narragansett RI 02882

Web version posted April 12, 2001

Citation: Kohler NE, Casey JG, Turner PA. 1996. Length-length and length-weight relationships for 13 shark species from the Western North Atlantic. US Dep Commer, NOAA Tech Memo NMFS NE 110; 22 p.

Information Quality Act Compliance: In accordance with section 515 of Public Law 106-554, the Northeast Fisheries Science Center completed both technical and policy reviews for this report. These predissemination reviews are on file at the NEFSC Editorial Office.

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The rapid expansion of sport and commercial fisheries for sharks in the western North Atlantic has created the need to manage the stocks of several species of large sharks.  In response to this need, a fishery management plan (FMP) for sharks within the U.S. Exclusive Economic Zone of the Atlantic Ocean (U.S. Department of Commerce 1992) was implemented in 1993.  The 39 shark species included in the FMP are not managed on an individual species basis, but are aggregated into three species groups -- large coastal, small coastal, and pelagic.  Basic biological data needed for stock assessment are lacking for many of these Atlantic sharks, including size values (i.e., minimum, maximum, and average) and size relationships/conversions (i.e., length-to-weight and fork length-to-total length).  These data are essential for understanding growth rate, age structure, and other aspects of population dynamics.

Size conversions have a practical value in fisheries.  One measure currently in practice at nearly all shark tournaments on the Atlantic Coast is the establishment of minimum size limits, usually a minimum weight.  Since sizes must be estimated at sea, means for converting lengths to weights are essential to anglers.  Moreover, the National Marine Fisheries Service (NMFS) conducts an extensive Atlantic Shark Tagging Program using volunteer assistance of recreational and commercial fishermen.  Commercial fishermen generally are more confident in estimating the weight of sharks being released, while recreational fishermen estimate lengths.  Conversions are needed to change these estimates into common size units for analysis.

Thus, in response to the immediate needs of tournament officials and fishermen, and for management initiatives, we present length and weight data for 13 species of large Atlantic sharks collected over a 29-yr period by the NMFS Apex Predator Investigation (API) at Narragansett, RI.


Length and weight data were collected from sharks caught by recreational and commercial fishermen and by biologists along the U.S. Atlantic Coast from the Gulf of Maine to the Florida Keys during 1961-89.  Sharks were caught primarily on rod and reel at sport fishing tournaments and on longline gear aboard research vessels and commercial fishing boats.  Some data were obtained from sharks that were harpooned or taken in gill nets.  Measurements from a white shark captured off Rhode Island in 1991 were also included in the analysis because of the specimen’s unusually large size.  Data were obtained opportunistically throughout each year, but most (88%) were collected during June-August off the northeastern United States between North Carolina and Massachusetts.  Only lengths and weights measured by the authors and other members of the API or by cooperating biologists are included in this report.  Measurements of embryos and fish known to be pregnant were excluded from the data set.

All lengths were taken with a metal measuring tape to the nearest centimeter in a straight line along the body axis with the caudal fin placed in a natural position.  Fork length (FL) was measured from the tip of the snout to the fork of the tail.  Total length (TL) is defined as the distance from the snout to a point on the horizontal axis intersecting a perpendicular line extending downward from the tip of the upper caudal lobe to form a right angle  (Figure 1).

Total weight (WT) of each shark was measured to the nearest pound and converted to kilograms.  The majority of fish were weighed while hanging by the caudal peduncle which allowed any water in the stomach and, in some cases, stomach contents to drain out prior to weighing.  Many fish were examined internally; if unusually large amounts of water or contents were found in the stomach or abdominal cavity, the weights of such were subtracted from the overall weight to obtain a more accurate measurement.

Fork length-to-total length relationships for 13 shark species (n = 5065) were determined by the method of least squares to fit a simple linear regression model.  Linear regressions of fork length-to-total length were calculated with their corresponding regression coefficients, sample sizes, and mean lengths.  These data are combined into four family groups:  Alopiidae (thresher sharks), Lamnidae (mackerel sharks), Carcharhinidae (requiem sharks), and Sphyrnidae (hammerhead sharks).  These combined data are then graphed for comparison.

An allometric length-weight equation was calculated using the method of Pienaar and Thomson (1969) for fitting a nonlinear regression model by least squares.  The form of the equation is WT = (a)FLb, where WT = total weight (kg), FL = fork length (cm), and a and b are constants for each species.  Length-weight relationships, mean lengths and weights, and size ranges were determined for 13 shark species (n = 9512).  Literature values for maximum fork length and fork length at maturity were also included.  These length-weight relationships were graphed with the size-at-maturity estimates indicated on each figure.  Weight (in pounds) was calculated for every 6 inches (15 cm) of length over our size range of each of the 13 shark species to construct a chart that can be used by anglers and tournament officials for setting minimum size limits on their catches.

In addition to metric units (i.e., centimeters and kilograms), figure scales are also shown in English units (i.e., feet and pounds) to make them more useful for U.S. tournament officials, anglers, and commercial fishermen.  Regressions of the length-weight equations expressed logarithmically were tested for significant differences (p<0.05) between males and females using an analysis-of-covariance test for homogeneity of slopes.

Fork length is used throughout this report as the basis for all conversions and comparisons.  We have found fork length to be a more precise measurement.  For comparison purposes, all values published elsewhere as total lengths were converted to fork lengths using the species’ equations presented in this paper.

Minimum sizes at maturity reported here are from published accounts with their original sources referenced, with the exception of the thresher shark (Alopias vulpinus) and white shark (Carcharodon carcharias).  Minimum size at maturity for the thresher shark and the male white shark were determined by H.L. Pratt, Jr. (pers. comm.; Nat. Mar. Fish. Serv., Narragansett, RI, May 1993), using the following criteria:  smallest male with calcified claspers that rotate at the base, and smallest gravid female.  When considerable variation occurred among published accounts, traditional sizes at maturity were chosen primarily from Atlantic populations.  Maximum sizes and maximum sizes at birth used here are summarized in Pratt and Casey (1990).


Linear regressions of fork length-to-total length for the 13 shark species are presented in Table 1, and linear regressions for the four shark family groups are portrayed in Figure 2.  Slopes of the regression lines of the four families decrease with increasing length of the upper caudal lobe (Figure 2).  The mackerel sharks (line 1) have lunate tails with the upper and lower caudal lobes almost equal in size.  The requiem (line 2), hammerhead (line 3), and thresher (line 4) sharks have heterocercal tails with the upper lobe longer than the lower.  The latter group have very long upper caudal lobes with the fork length approximately 60% of the total length.  Fork length represents 92%, 84%, and 77% of total length for mackerel, requiem, and hammerhead sharks, respectively.

Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15

A total of 9512 sharks representing 13 species were measured, sexed, and weighed.  There were no significant differences in slope or intercept of the length-weight relationships between males and females for any of the species.  Therefore, one equation, calculated with the sexes combined, was used to represent the data for each species (Figures 3-15 [accessible via the table on the right]; Table 2).

Size at maturity for males and females is difficult to determine for pelagic sharks, and can vary in different parts of the world (Pratt and Casey 1990).  The discrepancy is due, in part, to the use of variable criteria in determining a precise length at sexual maturity (Springer 1960; Clark and von Schmidt 1965; Pratt 1979), and thus maturity is often reported as a size range rather than a specific length.  An individual author’s definition of maturity is sometimes ambiguous or obscure.  The sizes at maturity (Table 3) are from multiple reference sources, and therefore may be mixed in definition and criteria.  The original published sources should be consulted for the basis for defining sexual maturity among different authors.

An attempt was made to obtain samples representative of the full size range of each species.  Minimum, maximum, and mean lengths and weights by species of sharks examined in this study are reported (Table 1 and Table 3).  A reliable maximum size is difficult to verify.  Lengths and/or weights for large fish are often reported inaccurately, and published accounts usually qualify maximum lengths with “probably reach,” “possibly to,” or “may grow up to.”  Maximum lengths (FL) reported in Pratt and Casey (1990) are included for comparison with sizes measured in this study (Table 3).  With the exception of the porbeagle (Lamna nasus) and tiger shark (Galeocerdo cuvier), our data are within 62 cm (2.5 ft) of published maximum sizes.  The porbeagle is less common in our study area; fewer specimens were examined (< 30), and therefore the full size range of this species is not represented.  Although the tiger shark is purported worldwide to grow to 469 cm FL (15.4 ft) (Castro 1983; Compagno 1984; Pratt and Casey 1990), Atlantic specimens may not attain that size.  Our longest tiger shark was 339 cm FL (11.1 ft) (Table 3).  Maximum reported length examined by Branstetter (1981) in a study of tiger sharks in the north central Gulf of Mexico was 346 cm FL (11.4 ft).  Maximum reported length for the U.S. Atlantic Coast is 391 cm FL (12.8 ft) (Bigelow and Schroeder 1948).  These lengths are more in agreement with individuals sampled in this study.

Specimens from three shark species exceeded the maximum reported lengths (Table 3):  sandbar shark (Carcharhinus plumbeus), shortfin mako (Isurus oxyrinchus), and scalloped hammerhead (Sphyrna lewini).  The 211 cm FL (6.9 ft) female sandbar shark in this study (Table 1) was measured by one of the authors (J. Casey) and is the largest measured sandbar reported to date.  This fish was caught in September 1964 by a sport fisherman approximately 10 mi east of Asbury Park, NJ.  Unfortunately, the fish was not weighed.  Two shortfin makos measured in this study were longer than the 336 cm FL (11.0 ft) maximum size fish published in the literature.  Both of these fish were 338 cm FL (11.1 ft) females caught by sport fishermen south of Montauk Point, NY.  One was landed in July 1977 and weighed 471 kg (1039 lb).  The other was caught in August 1979 and weighed 382 kg (841 lb).  The largest scalloped hammerhead [243 cm (8.0 ft) FL and 166 kg (365 lb)] was measured at a sportfishing tournament in July 1985, and was caught 36 mi southeast of Highlands, NJ.

The lower ends of the length-weight curves also compare well with published estimates of size at birth for each species of shark.  Pratt and Casey (1990) give maximum size at birth in TL for 11 of the 13 species of sharks sampled here; all except the thresher shark are within 40 cm (15.7 inches) of those sizes.  Our smallest thresher shark is 64 cm (25.2 inches) larger than the reported birth size.

All of the larger fish were female with the exception of the white shark (Figure 5) and blue shark (Prionace glauca) (Figure 14).  The larger size attained by females is typical of sharks in general (Pratt and Casey 1983; Hoenig and Gruber 1990), and thus larger female blue and white sharks very likely occur outside of our western North Atlantic sampling area which only covers a small portion of their extensive oceanic range.  

Factors Affecting Weight

Weights of individual sharks of the same length may differ depending on several factors, including the amount of stomach contents, stage of maturity, liver weight, and body condition.  Effects of stomach contents on the weight of the fish were minimal in this study.  In many instances, the sharks everted their stomachs prior to being weighed.  For the bigger fish, when large amounts of food were present, the contents’ weight was subtracted to obtain the total body weight.  Since not every shark was examined internally, some pregnant fish may have been inadvertently included in the data base.

Differences in body weight also reflect differences in body condition.  Sharks have large livers which store high-energy, fatty acids for buoyancy and use as a food reserve (Bone and Roberts 1969; Oguri 1990).  The weight of this organ is thus a good indicator of the health or condition of a shark (Springer 1960; Cliff et al. 1989).  The liver is the largest organ by weight in the shark and can vary from 2 to 24% of body weight depending on the species (Cliff et al. 1989; Winner 1990).  This variation in liver size accounted for the majority of the weight difference in individuals of the same species with corresponding lengths.

Of the eight largest white sharks, six were measured for liver weight; those liver weights ranged from 14.6 to 22.7% of body weight (hepatosomatic index or HSI) (Table 4).  The 458 cm (15.0 ft) FL white shark in this group had the lowest HSI value (14.6%) although it was longer than four heavier fish.  The difference in body weight between the 458 cm (15.0 ft) FL and the 463 cm (15.2 ft) FL fish is 360 kg (794 lb).  When the body weights of these two fish -- minus their liver weights -- are compared, the difference is reduced to 239 kg (526 lb).  Thus, liver weight accounted for 34% of the body weight difference between these two sharks of similar length.
The same is true for large shortfin makos.  The HSI for one of the longest makos [338 cm (11.1 ft) FL and 382 kg (841 lb)] was 5.4%, as contrasted with 17.9% for the 323 cm (10.6 ft) FL fish weighing 490 kg (1080 lb).  When the body weights of these two fish -- minus their liver weights -- are compared, the difference is reduced from 108 kg (239 lb) to 41 kg (91 lb).


The data for this study could not have been collected without the help and cooperation of thousands of fishermen who allowed us to measure their shark catches over the last 29 yr.  The scientists, officers, and crew of several research vessels also assisted in obtaining specimens during sampling cruises.  We are particularly grateful to tournament officials and participants from New York, New Jersey, Massachusetts, and Rhode Island from whose catches a large part of the data were collected.  Further, we would like to thank the past and present members of the Apex Predator Investigation, including Chuck Stillwell, Lisa J. Natanson, Ruth Briggs, H.L. Pratt, Jr., and Gregg Skomal, for their assistance and support.


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Bone, Q.; Roberts, B.L.  1969.  The density of elasmobranchs.  J. Mar. Biol. Assoc. U.K. 49:913-937.

Branstetter, S.  1981.  Biological notes on the sharks of the north central Gulf of Mexico.  Contrib. Mar. Sci. 24:13-34.

Branstetter, S.  1987.  Age, growth and reproductive biology of the silky shark, Carcharhinus falciformis, and the scalloped hammerhead, Sphyrna lewini, from the northwestern Gulf of Mexico.  Environ. Biol. Fishes 19:161-173.

Branstetter, S.; Musick, J.A.; Colvocoresses, J.A.  1987.  Age and growth estimates of the tiger shark, Galeocerdo cuvieri, from off Virginia and from the northwestern Gulf of Mexico. Fish. Bull. (U.S.) 85:269-279.

Casey, J.G.; Pratt, H.L., Jr.  1985.  Distribution of the white shark, Carcharodon carcharias, in the western North Atlantic.  Mem. South. Calif. Acad. Sci. 9:2-14.

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Hoenig, J.M.; Gruber, S.H.  1990.  Life-history patterns in the elasmobranchs: implications for fisheries management. In: Pratt, H.L., Jr.; Gruber, S.H.; Taniuchi, T., eds.  Elasmobranchs as living resources: advances in biology, ecology, systematics and status of the fisheries.  NOAA Tech. Rep. NMFS 90:1-16.

Oguri, M.  1990.  A review of selected physiological characteristics unique to elasmobranchs.  In: Pratt, H.L., Jr.; Gruber, S.H.; Taniuchi, T., eds.  Elasmobranchs as living resources: advances in biology, ecology, systematics and status of the fisheries.  NOAA Tech. Rep. NMFS 90:49-54.

Pienaar, L.V.; Thomson, J.A.  1969.  Allometric weight-length regression model.  J. Fish. Res. Board Can. 26:123-131.

Pratt, H.L., Jr.  1979.  Reproduction in the blue shark, Prionace glaucaFish. Bull. (U.S.) 77:445-469.

Pratt, H.L., Jr.; Casey, J.G.  1983.  Age and growth of the shortfin mako, Isurus oxyrinchus, using four methods. Can. J. Fish. Aquat. Sci. 40:1944-1957.

Pratt, H.L., Jr.; Casey, J.G.  1990.  Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden’s method of estimating growth-parameters.  In: Pratt, H.L., Jr.; Gruber, S.H.; Taniuchi, T., eds.  Elasmobranchs as living resources: advances in biology, ecology, systematics and status of the fisheries.  NOAA Tech. Rep. NMFS 90:97-109.

Randall, J.E.  1987.  Refutation of lengths of 11.3, 9.0, and 6.4 m attributed to the white shark, Carcharodon carcharias. Calif. Fish Game 73(3):163-168.

Springer, S.  1960.  Natural history of the sandbar shark Eulamia milbertiFish. Bull. (U.S.) 61:1-38.

Stevens, J.D.  1983.  Observations on reproduction in the shortfin mako, Isurus oxyrinchusCopeia 1983(1):126-130.

U.S. Department of Commerce.  1992.  Fishery management plan for sharks of the Atlantic Ocean.  Silver Spring, MD: National Marine Fisheries Service; 160 p.

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API = (NMFS Northeast Fisheries Science Center) Apex Predator Investigation
FL = fork length
FMP = fishery management plan
HSI = hepatosomatic index
NMFS = (NOAA) National Marine Fisheries Service
TL = total length
WT = body weight
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